Monotonicity: The first derivative test shows that the curve is increasing throughout $(-\infty, \infty)$

Step 5:

Special points : The curve is concave downward in $(-\infty,0)$ and concave upward in $(0, \infty)$. Since $y^x=6 x < 0$ for $ x < 0 $ and $y''=6x > 0$ for $ x > 0$ and $y''=0$ for $x=0,$ yielding $(0,0)$ as a point of inflection